A 86 kg clock initially at rest on a horizontal floor requires a 649 N horizontal force to set it in motion. After the clock is in motion, a horizontal force of 517 N keeps it moving with a constant velocity.
(a) Find μs between the clock and the floor.
(b) Find μk between the clock and the floor.
To find the coefficients of friction, we need to use Newton's laws of motion. Let's break down the problem and solve it step by step.
(a) To find the coefficient of static friction (μs), we need to calculate the maximum force of friction that exists before the clock starts moving.
We are given:
Mass of the clock (m) = 86 kg
Force required to set the clock in motion (F) = 649 N
The maximum force of friction (Ff_max) can be calculated using the formula:
Ff_max = μs * N
Where N is the normal force acting on the clock, which is equal to the weight of the clock (mg), where g is the acceleration due to gravity.
So the equation becomes:
Ff_max = μs * mg
Now, we can substitute the given values into the equation:
649 N = μs * (86 kg * 9.8 m/s^2)
Simplifying the equation:
μs = 649 N / (86 kg * 9.8 m/s^2)
Calculating the value:
μs ≈ 0.77
Therefore, the coefficient of static friction (μs) between the clock and the floor is approximately 0.77.
(b) To find the coefficient of kinetic friction (μk), we need to calculate the force of friction when the clock is moving with a constant velocity.
We are given:
Force required to keep the clock moving (F) = 517 N
The force of kinetic friction (Ff_k) is given by:
Ff_k = μk * N
Using the same logic as before, we can substitute the values into the equation:
517 N = μk * (86 kg * 9.8 m/s^2)
Simplifying the equation:
μk = 517 N / (86 kg * 9.8 m/s^2)
Calculating the value:
μk ≈ 0.61
Therefore, the coefficient of kinetic friction (μk) between the clock and the floor is approximately 0.61.